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A/D conversion with imperfect quantizers

机译：具有不完善量化器的A / D转换

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摘要

This paper analyzes mathematically the effect of quantizer threshold imperfection commonly encountered in the circuit implementation of analog-to-digital (A/D) converters such as pulse code modulation (PCM) and sigma-delta (/spl Sigma//spl Delta/) modulation. /spl Sigma//spl Delta/ modulation, which is based on coarse quantization of oversampled (redundant) samples of a signal, enjoys a type of self-correction property for quantizer threshold errors (bias) that is not shared by PCM. Although "classical" /spl Sigma//spl Delta/ modulation is inferior to PCM in the rate-distortion sense, this robustness feature is believed to be one of the reasons why /spl Sigma//spl Delta/ modulation is preferred over PCM in A/D converters with imperfect quantizers. Motivated by these facts, other encoders are constructed in this paper that use redundancy to obtain a similar self-correction property, but that achieve higher order accuracy relative to bit rate compared to classical /spl Sigma//spl Delta/. More precisely, two different types of encoders are introduced that exhibit exponential accuracy in the bit rate (in contrast to the polynomial-type accuracy of classical /spl Sigma//spl Delta/) while possessing the self-correction property.
机译：本文用数学方法分析了在诸如脉冲编码调制（PCM）和sigma-delta（/ spl Sigma // spl Delta /）等模数（A / D）转换器的电路实现中通常遇到的量化器阈值不完善的影响调制。 / spl Sigma // spl Delta /调制基于信号的过采样（冗余）样本的粗量化，它具有针对PCM不共享的量化器阈值误差（偏置）的一种自校正属性。尽管“经典”的/ spl Sigma // spl Delta /调制在速率失真方面不如PCM，但这种鲁棒性被认为是/ spl Sigma // spl Delta /调制优于PCM的原因之一。具有不完善量化器的A / D转换器。基于这些事实，本文构造了其他编码器，这些编码器使用冗余来获得类似的自校正特性，但是与经典的/ spl Sigma // spl Delta /相比，其比特率方面的精度更高。更精确地，引入了两种不同类型的编码器，它们在具有自校正特性的同时，在比特率中表现出指数精度（与经典的/ spl Sigma // spl Delta /的多项式类型的精度相反）。

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